H∞ control for singularly perturbed systems with unknown dynamics: An inverse reinforcement learning scheme

The inverse H∞ control problem for linear singularly perturbed systems (SPSs) with unknown system dynamics is investigated in this paper. First, a full-order model is adopted to characterize the coexistence of fast and slow modes in SPSs. Unlike existing studies on the optimal control of SPSs that rely on a predefined value function, a novel inverse learning scheme is developed, through which the learner iteratively reconstructs an expert-equivalent cost function and updates its control policy from expert demonstrations. To alleviate the numerical ill-conditioning induced by the singular perturbation, a well-posed update structure is further introduced. Furthermore, a model-free online data-driven inverse H∞ learning scheme is developed, so that the learner gain can be updated directly from measured state and input data without requiring explicit knowledge of the system dynamics. Theoretical analysis establishes the convergence of the proposed learning scheme and the validity of the data-driven implementation under the required rank condition. Finally, a permanent magnet synchronous motor example is provided to validate the effectiveness of the proposed method, demonstrating good learning accuracy, convergence performance, and applicability.